Deep Learning of Phase Transitions for Quantum Spin Chains from Correlation Aspects

TL;DR

This paper employs machine learning on spin-spin correlation functions to accurately map quantum phase diagrams of spin chains, revealing new features and phase boundaries, and distinguishing phase transitions through unsupervised learning techniques.

Contribution

It extends previous ML methods to magnetic systems, introducing relevant correlation functions and applying unsupervised learning to identify phase boundaries and transition types.

Findings

Accurate phase diagrams for XY and XXZ spin chains.

Identification of new features in phase transitions.

Unsupervised learning distinguishes continuous and discontinuous transitions.

Abstract

Using machine learning (ML) to recognize different phases of matter and to infer the entire phase diagram has proven to be an effective tool given a large dataset. In our previous proposals, we have successfully explored phase transitions for topological phases of matter at low dimensions either in a supervised or an unsupervised learning protocol with the assistance of quantum information related quantities. In this work, we adopt our previous ML procedures to study quantum phase transitions of magnetism systems such as the XY and XXZ spin chains by using spin-spin correlation functions as the input data. We find that our proposed approach not only maps out the phase diagrams with accurate phase boundaries, but also indicates some new features that have not observed before. In particular, we define so-called relevant correlation functions to some corresponding phases that can always distinguish between those and their neighbors. Based on the unsupervised learning protocol we proposed [Phys. Rev. B 104, 165108 (2021)], the reduced latent representations of the inputs combined with the clustering algorithm show the connectedness or disconnectedness between neighboring clusters (phases), just corresponding to the continuous or disrupt quantum phase transition, respectively.